Essays on Finite Mixture Models

Essays over finite mixture modellen

Finite mixture distributions are a weighted average of a ¯nite number of distributions.
The latter are usually called the mixture components. The weights are usually described
by a multinomial distribution and are sometimes called mixing proportions. The mixture
components may be the same type of distributions with di®erent parameter values but
they may also be completely di®erent distributions (Everitt and Hand, 1981; Titterington
et al., 1985). Therefore, ¯nite mixture distributions are very °exible for modeling data.
They are frequently used as a building block within many modern econometric models.
The speci¯cation of the mixture distribution depends on the modeling problem at hand.
In this thesis, we introduce new applications of ¯nite mixtures to deal with several
di®erent modeling issues. Each chapter of the thesis focusses on a speci¯c modeling
issue. The parameters of some of the resulting models can be estimated using standard
techniques but for some of the chapters we need to develop new estimation and inference
methods. To illustrate how the methods can be applied, we analyze at least one empirical
data set for each approach. These data sets cover a wide range of research ¯elds, such as
macroeconomics, marketing, and political science. We show the usefulness of the methods
and, in some cases, the improvement over previous methods in the literature.